A Hölder estimate for nonlinear parabolic systems of \(p\)-Laplacian type
type: Item
instance of: scholarly article
title: A Hölder estimate for nonlinear parabolic systems of \(p\)-Laplacian type
zbMATH Open document ID: 1273.35173
author: Masashi Misawa
published in: Journal of Differential Equations
publication date: 2012-12-20T00:00:00Z
review text: The Hölder continuity of the solution \(u= (u^1,u^2,\dots, u^n)\) of the parabolic system \[ {\partial u^j\over\partial t}- \text{div}(|Du|^{p-2} Du^j)= \text{div}(|g|^{p-2} g^j)+ F^j(x,t,Du), \] \(j= 1,2,\dots, n\), is proved under fairly general assumptions on the right-hand side. Here \(p>{2N\over N+2}\) and the functions are defined in a bounded domain in \(\mathbb{R}^{N+1}\). The proof of the main theorem about local Hölder continuity is based on the ``Campanato perturbation'' and diBenedetto's intrinsic scaling. This extends results of diBenedetto, Y.-Z. Chen, Acerbi, and Mingione.
reviewed by: Peter Lindqvist
Mathematics Subject Classification ID: 35K92
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 6117526
zbMATH Keywords: regularity theory
zbMATH Keywords: \(p\)-Laplacian systems
MaRDI profile type: Publication
full work available at URL: j.jde.2012.10.001
OpenAlex ID: W2031390689
DOI: 10.1016/J.JDE.2012.10.001
description: scientific article; zbMATH DE number 6117526